A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In optical projection lithography, a high-powered projection beam is generally used in order to reduce the time taken for an exposure and hence increase the throughput of the apparatus. Because the elements of the projection system used to project an image of the pattern onto the substrate are not perfectly transmissive or reflective, some energy from the beam will be absorbed. This energy causes the elements of the projection system to heat up, in spite of the provision of cooling systems, and change their shape or relative position. Any such changes introduce aberrations into the projected wave-front. This problem is generally known as “lens heating” as it is most problematic in refractive elements such as lenses.
In known attempts to address lens heating, the effects of lens heating are predicted on an exposure-by-exposure basis and adjustable elements in the projection system are adjusted to compensate. It is common to describe the aberrations caused by lens heating in terms of phase variations expressed in Zernike polynomials and to make adjustments to corresponding “knobs” provided for the projection system. However, it is difficult to provide an adjustable element that affects aberrations in only a single Zernike polynomial so a control system may be provided that presents virtual “knobs” corresponding one to one to Zernike polynomials and which for a given input adjusts several elements in the projection system whose net effect is the desired adjustment.
With the constant desire to improve image quality and resolution, improvements in compensation for lens heating effects are desired. In particular, steep phase gradients are often observed that cannot be expressed in low-order Zernike polynomials and are not well predicted or corrected for by known techniques. Flare and non-concentric phase-stripes due to mask manufacturing methods also produce aberrations that are difficult to correct.